Kitchen ceiling water damage from bathroom sink overflow above: best way to repair properly?

Bathroom sink overflowed onto the floor and came through the kitchen ceiling below. The drywall sagged and we drained it. We’ve been running fans and a dehumidifier since. We’re renters and want to handle this responsibly. We’re figuring out what to bring the landlord: a repair plan, a cost estimate, or an offer to pay for it.

Questions:

How do we confirm the joists and subfloor are actually dry?

Is this a cut-out-and-replace job or patchable?

Rough cost for a pro vs. DIY?

Thank you so much 🙏

New-Good-9194
1 | 9 hours ago